(6+6i)x=-3-3i

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Solution for (6+6i)x=-3-3i equation:


Simplifying
(6 + 6i) * x = -3 + -3i

Reorder the terms for easier multiplication:
x(6 + 6i) = -3 + -3i
(6 * x + 6i * x) = -3 + -3i

Reorder the terms:
(6ix + 6x) = -3 + -3i
(6ix + 6x) = -3 + -3i

Solving
6ix + 6x = -3 + -3i

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '3i' to each side of the equation.
6ix + 3i + 6x = -3 + -3i + 3i

Reorder the terms:
3i + 6ix + 6x = -3 + -3i + 3i

Combine like terms: -3i + 3i = 0
3i + 6ix + 6x = -3 + 0
3i + 6ix + 6x = -3

Add '-6x' to each side of the equation.
3i + 6ix + 6x + -6x = -3 + -6x

Combine like terms: 6x + -6x = 0
3i + 6ix + 0 = -3 + -6x
3i + 6ix = -3 + -6x

Reorder the terms:
3 + 3i + 6ix + 6x = -3 + -6x + 3 + 6x

Reorder the terms:
3 + 3i + 6ix + 6x = -3 + 3 + -6x + 6x

Combine like terms: -3 + 3 = 0
3 + 3i + 6ix + 6x = 0 + -6x + 6x
3 + 3i + 6ix + 6x = -6x + 6x

Combine like terms: -6x + 6x = 0
3 + 3i + 6ix + 6x = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + i + 2ix + 2x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + i + 2ix + 2x)' equal to zero and attempt to solve: Simplifying 1 + i + 2ix + 2x = 0 Solving 1 + i + 2ix + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + i + 2ix + -1 + 2x = 0 + -1 Reorder the terms: 1 + -1 + i + 2ix + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i + 2ix + 2x = 0 + -1 i + 2ix + 2x = 0 + -1 Combine like terms: 0 + -1 = -1 i + 2ix + 2x = -1 Add '-2x' to each side of the equation. i + 2ix + 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 i + 2ix + 0 = -1 + -2x i + 2ix = -1 + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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